Moreover, returning to Anthony
andWalshaw’s (2009) ten principles of effective teaching and acknowledging that our analyses
were framed by the PAF, neither data set indicated evidence of, for example, teachers building
on students’ thinking, facilitating mathematical communication or assessing formatively.
Interestingly, it could be argued that all four lesson sequences incorporated evidence of
teachers encouraging the development of mathematical language, employing worthwhile
mathematical tasks, making appropriate mathematical connections and selecting appropriate
tools and representations. However, whether such didactical strategies were managed in ways
that would facilitate learning in the manner envisaged by Anthony and Walshaw is unlikely